296 research outputs found
Distribution of Values of Quadratic Forms at Integral Points
The number of lattice points in -dimensional hyperbolic or elliptic shells
, which are restricted to rescaled and growing domains
, is approximated by the volume. An effective error bound of order
for this approximation is proved based on Diophantine
approximation properties of the quadratic form . These results allow to show
effective variants of previous non-effective results in the quantitative
Oppenheim problem and extend known effective results in dimension to
dimension . They apply to wide shells when is growing with
and to positive definite forms . For indefinite forms they provide explicit
bounds (depending on the signature or Diophantine properties of ) for the
size of non-zero integral points in dimension solving the
Diophantine inequality and provide error bounds
comparable with those for positive forms up to powers of .Comment: Section 4 and 7, also bounds in sections 6 have been revised and
greatly extended, e.g. box artifacts for wide hyperbolic shells are removed.
Applications to Diophantine lattices are revised and reduced exponents for
solutions of Diophantine inequalities depending on signature are proved for
large , similar to integral forms. For small larger exponents are now
required in Th.1.
Why municipalities grow: The influence of fiscal incentives on municipal land policies in Germany and the Netherlands
It is generally assumed that municipalities attract residents and businesses as a result of intermunicipal competition for tax revenues. This growth-oriented behaviour poses a serious problem considering internationally acknowledged goals to limit land take. Nonetheless, research on how fiscal incentives affect municipal land policies is scarce. Adapting a neoinstitutionalist approach, we compare the two contrasting fiscal systems of Germany and the Netherlands. While clear incentives can be deducted from the different sources of municipal income, complex balancing measurements and consequential infrastructure investments make it difficult to predict a project’s profitability. According to the perspective of planning practitioners in municipalities around the growth centres of Utrecht and Berlin interviewed for this study, local pressures force them to keep allocating new building sites. In order to create effective policies to limit land take, it is important to understand not only
the influence of fiscal incentives but also of place-specific pressures on municipal land policies
The role of azacitidine in the management of myelodysplastic syndromes (MDS)
Myelodysplastic syndromes (MDS) are a group of common bone marrow disorders characterized by ineffective hematopoiesis, peripheral cytopenias, and a propensity for transformation to acute myeloid leukemia (AML). For many years, the main treatment option for MDS was best supportive care which alleviates symptoms but has no effect on the natural course of the disease. The recent approval of the demethylating agent azacitidine represents a significant advance in the treatment of MDS. The results of two randomized trials with azacitidine have shown an overall response rate between 40% and 60%, an improved quality of life, a reduced risk of transformation to AML and a definite survival advantage compared to best supportive care or low-dose chemotherapy. Current data on azacitidine and its place in the treatment of MDS are reviewed
On the "generalized Generalized Langevin Equation"
In molecular dynamics simulations and single molecule experiments,
observables are usually measured along dynamic trajectories and then averaged
over an ensemble ("bundle") of trajectories. Under stationary conditions, the
time-evolution of such averages is described by the generalized Langevin
equation. In contrast, if the dynamics is not stationary, it is not a priori
clear which form the equation of motion for an averaged observable has. We
employ the formalism of time-dependent projection operator techniques to derive
the equation of motion for a non-equilibrium trajectory-averaged observable as
well as for its non-stationary auto-correlation function. The equation is
similar in structure to the generalized Langevin equation, but exhibits a
time-dependent memory kernel as well as a fluctuating force that implicitly
depends on the initial conditions of the process. We also derive a relation
between this memory kernel and the autocorrelation function of the fluctuating
force that has a structure similar to a fluctuation-dissipation relation. In
addition, we show how the choice of the projection operator allows to relate
the Taylor expansion of the memory kernel to data that is accessible in MD
simulations and experiments, thus allowing to construct the equation of motion.
As a numerical example, the procedure is applied to Brownian motion initialized
in non-equilibrium conditions, and is shown to be consistent with direct
measurements from simulations
Information structure
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From Equilibrium to Steady-State Dynamics after Switch-On of Shear
A relation between equilibrium, steady-state, and waiting-time dependent
dynamical two-time correlation functions in dense glass-forming liquids subject
to homogeneous steady shear flow is discussed. The systems under study show
pronounced shear thinning, i.e., a significant speedup in their steady-state
slow relaxation as compared to equilibrium. An approximate relation that
recovers the exact limit for small waiting times is derived following the
integration through transients (ITT) approach for the nonequilibrium
Smoluchowski dynamics, and is exemplified within a schematic model in the
framework of the mode-coupling theory of the glass transition (MCT). Computer
simulation results for the tagged-particle density correlation functions
corresponding to wave vectors in the shear-gradient directions from both
event-driven stochastic dynamics of a two-dimensional hard-disk system and from
previously published Newtonian-dynamics simulations of a three-dimensional
soft-sphere mixture are analyzed and compared with the predictions of the
ITT-based approximation. Good qualitative and semi-quantitative agreement is
found. Furthermore, for short waiting times, the theoretical description of the
waiting time dependence shows excellent quantitative agreement to the
simulations. This confirms the accuracy of the central approximation used
earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102,
135701). For intermediate waiting times, the correlation functions decay faster
at long times than the stationary ones. This behavior is predicted by our
theory and observed in simulations.Comment: 16 pages, 12 figures, submitted to Phys Rev
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